Question

Find the x-intercepts of the parabola with vertex (1, -9) and y intercept at (0, -6).

Answer 1

hello :
the parabola's equation is : f(x) = a(x-1)²-9
the coefficient of the squared expression in the parabola's equation is : a
but ; f(0) = -6 ...  ( y-intercepts (0,-6) )

-6 = a(0-1)²-9
-6 =a -9

a=3
f(x) = 3(x-1)²-9

 the x-intercepts  when : f(x) =0
3(x-1)²-9 =0
(x-1)² =3
x-1 = √3)   or x-1 = -√3) 

x= 1 +√3   or  x= 1 -√3 are  the x-intercepts